Electron. J. Diff. Eqns., Vol. 2009(2009), No. 46, pp. 1-8.

Weak almost periodic and optimal mild solutions of fractional evolution equations

Amar Debbouche, Mahmoud M. El-Borai

In this article, we prove the existence of optimal mild solutions for linear fractional evolution equations with an analytic semigroup in a Banach space. As in [16], we use the Gelfand-Shilov principle to prove existence, and then the Bochner almost periodicity condition to show that solutions are weakly almost periodic. As an application, we study a fractional partial differential equation of parabolic type.

Submitted March 10, 2009. Published March 30, 2009.
Math Subject Classifications: 34G10, 26A33, 35A05, 34C27, 35B15.
Key Words: Linear fractional evolution equation; Optimal mild solution; weak almost periodicity; analytic semigroup.

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Amar Debbouche
Faculty of Science, Guelma University
Guelma, Algeria
email: amar_debbouche@yahoo.fr
Mahmoud M. El-Borai
Faculty of Science, Alexandria University
Alexandria, Egypt
email: m_m_elborai@yahoo.com

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